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Data adaptive multi-scale representations for image analysis
Author(s): Julia Dobrosotskaya; Weihong Guo
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Paper Abstract

Data adaptive tight frame methods have been proven a powerful sparse approximation tool in a variety of settings. We introduce a model of a data adaptive representation that also provides a multi-scale structure. Our idea is to design a multi-scale frame representation for a given data set, with scaling properties similar to the ones of a wavelet basis, but without the necessary self-similar structure. The adaptivity provides better sparsity properties, using Besov-like norm structure both induces sparsity and helps in identifying important features. We focus on investigating the efficiency of a weighted l1 constraint in the context of sparse recovery from noisy data and compare it to the weighted l0 model alongside. Numerical experiments confirm that the recovered frame vectors assigned lower weights correspond to image elements of larger scale and lower local variation, thus indicating that weighted sparsity in natural images leads to a natural scale separation.

Paper Details

Date Published: 9 September 2019
PDF: 7 pages
Proc. SPIE 11138, Wavelets and Sparsity XVIII, 1113807 (9 September 2019); doi: 10.1117/12.2529695
Show Author Affiliations
Julia Dobrosotskaya, Case Western Reserve Univ. (United States)
Weihong Guo, Case Western Reserve Univ. (United States)


Published in SPIE Proceedings Vol. 11138:
Wavelets and Sparsity XVIII
Dimitri Van De Ville; Manos Papadakis; Yue M. Lu, Editor(s)

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